1. Field of the Invention
The invention relates generally to the field of well logging. More particularly, the invention relates to tools and methods for measuring electrical properties of a formation with anisotropy and/or invasion.
2. Background Art
Induction tools have been used for many years to measure the resistivity of earth formations surrounding a borehole in the presence of borehole fluids that may have invaded the formations. Induction logging tools measure the resistivity (or its inverse, conductivity) of the formation by inducing eddy currents in the formations in response to an AC transmitter signal. The eddy currents induce secondary magnetic fields that in turn induce voltages in receiver antennas. Because the magnitudes of the eddy currents depend on formation conductivities, the magnitudes of the received signals thus reflect the formation conductivities.
A typical induction tool includes at least two induction arrays having different spacings between the transmitters and the receivers for different depths of investigation (DOI). An example of such tools is disclosed in U.S. Pat. No. 3,067,383 issued to Tanguy. A minimal configuration of such tools includes two coil arrays for measuring at two different DOI: a deep array (ILD) and a medium array (ILM). The deep array is designed to “see” beyond the mud invaded zone in order to provide true formation resistivity (Rt). However, in order to determine the minimum parameters (the invaded zone resistivity, Rxo, the resistivity of the uninvaded zone, Rt, and the radius of invasion, ri) of a formation invaded by drilling fluids, at least three measurements at different depths of investigation are required. Historically, the third measurement (a shallow measurement) is provided by a focused electrode array. One such tool is disclosed in U.S. Pat. No. 3,329,889 issued to Tanguy. The shallow electrode measurement together with the medium (ILM) and deep (ILD) measurements provided by the induction arrays provide sufficient data to solve formation resistivities in a formation with a simple invasion profile. Such tools may not provide sufficient data for the determination of formation properties when the invasion profiles is complicated, e.g., more than one zone surrounding the borehole with different resistivities.
Therefore, multi-array tools have been introduced for the determination of formation resistivity in formations with more complex invasion profiles. Examples of multi-array tools include those disclosed in Hunka et al., “A New Resistivity Measurement System for Deep Formation Imaging and High-resolution Formation Evaluation, ” Paper SPE 20559, presented at the 65th SPE Annual Technical Conference and Exhibition, New Orleans, La., Sep. 23–26, 1990, and U.S. Pat. No. 5,157,605 issued to Chandler et al. The multiple arrays, having different spacings between the transmitter and the receiver, can provide measurements at different depths of investigation (DOI). Therefore, when mud invasion occurs to different extents (radii) in different layers, sufficient data may still be provided by such tools for solving formation electrical properties.
In addition to mud invasion, formation anisotropy can also complicate resistivity logging and interpretation. Formation anisotropy results from the manner in which formation beds were deposited by nature. Formations containing hydrocarbons often exhibit anisotropy in formation resistivity. In such formations, the horizontal conductivity, σh, (or resistivity, Rh) in a direction parallel to the bedding plane differs from the vertical conductivity, σv, (or resistivity, Rv) in a direction perpendicular to the bedding plane. In crossbedded reservoirs, the anisotropic resistivities may be better defined in two directions other than those that are parallel and perpendicular to the formation layers. For clarity of illustration, this description uses “horizontal” and “vertical” in a broad sense to describe the two orthogonal directions of the anisotropic resistivities, regardless of whether these directions are actually parallel or perpendicular to the bedding planes. The actual directions can be resolved by the inversion methods used in log analysis, for example the method to be described in FIG. 9.
Conventional induction logging tools, such as those described above, have their transmitters and receivers arranged in a manner such that their magnetic dipoles are aligned with the longitudinal axis of the tools. These longitudinal induction array tools induce eddy currents in loops that are perpendicular to the longitudinal axes of the tools. Therefore, these tools are sensitive only to the horizontal conductivity of the formations; they cannot provide a measure of vertical conductivity (or resistivity) or anisotropy.
To measure the vertical conductivity or anisotropy, new EM induction or propagation instruments typically include transmitter and/or receiver antennas that have their magnetic dipoles substantially perpendicular to the axis of the instrument. These tools with transverse induction arrays have good sensitivity to formation resistivity anisotropy. See e.g., Moran and Gianzero, “Effects of Formation Anisotropy on Resistivity Logging Measurements, ” Geophysics, 44, 1266–1286 (1979). Transverse induction arrays tools include triaxial array tools, which include three orthogonal transmitter coils and three receivers coils in the same orthogonal orientations. In operation, the tri-axial transmitter is energized in three orthogonal directions. Individual receiver coils aligned in the same three orthogonal directions then measure the voltages induced by eddy currents flowing in the surrounding formations. Examples of triaxial tools, for example, may be found in U.S. Pat. No. 3,510,757 issued to Huston, U.S. Pat. No. 5,781,436 issued to Forgang et al., U.S. Pat. No. 3,609,521, issued to Desbrandes, U.S. Pat. No. 4,360,777, issued to Segesman, and U.S. Pat. No. 6,553,314 issued to Kriegshäuser, et al. These triaxial array induction tools can determine the formation anisotropic resistivity as long as the formation is uninvaded or the invasion depth is shallow.
Although certain prior art tools are capable of measuring resistivities of formations with complex invasion profiles and others are good for formations with anisotropy, prior knowledge of the formation type is needed in order to choose a proper tool. It is desirable that EM induction or propagation logging tools are available to provide reliable measurements of formation resistivities without prior knowledge of formation anisotropy and/or invasion.